Answer:
--- Never true
--- Always true
---- Sometimes true
---- Sometimes true
Step-by-step explanation:
Given

Required
Determine if the following expression is always, sometimes of never true

Expand using cosine rule


So, we have:




Hence: (a) is never true

Expand using cosine rule


So, we have:



Hence: (b) is always true

If

Then:


Divide both sides by 2

(c) is only true for 
Hence: (c) is sometimes true

If

Then:


Divide both sides by 2

(d) is only true for 
Hence: (d) is sometimes true
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

so then we can say that

so we're really looking for the equation of a line whos slope is 9/2 and passes through (2 , 3)

now as far as the parallel line
keeping in mind that parallel lines have exactly the same slope, so we're really looking for the equation of a line whose slope is -2/9 and passes through (2 , 3)

The origin is (0,0)
slope = (y2 - y1) / (x2 - x1)
(-3,-2)....x1 = -3 and y1 = -2
(0,0)...x2 = 0 and y2 = 0
now we sub
slope = (0 - (-2) / (0 - (-3) = (0 + 2) / (0 + 3) = 2/3 <=
15 15 15 15 15 15 15 15 15 15
It should be 108,000 liters because if there are 60 seconds per minute and the pump was on for 39 mins, 60 x 30 = 1800
Then 1800 seconds times 60 liters per second equals 108,000 liters